It's very straightforward to keep your colonial nations under your heel.
If you have the Common Sense DLC, the best option is to develop them. Their land is garbage for the most part, and development efficiency is so that it costs next to nothing around when they become large enough to want to be free. So throw a few hundred monarch points every now and then into developing a bunch of their provinces to 10 to build extra factories or whatever else you think would be useful. Every single time you hit the button to develop your colonial nation, they get -5% liberty desire. It stacks -- hit the button 10 times and they've -50%. And it decays very slowly.
The other main way is to get them into debt. If you're loaded with cash, and you usually are by the time liberty desire is a problem, build a bunch of level 8 forts on your colonial nations to ensure that their expenses are way more than what they can afford. And then pay off their debts from time to time using the subject interaction menu, for a cumulative -10% (?) liberty desire per loan paid off that also decays very slowly -- albeit from a different decay pool. One caveat here is that the colonial nations will delete superfluous forts when running a deficit while at peace. I haven't tested but I'd surmise they do so only when the month ticks, like for war exhaustion reduction. But presumably you're seldom if ever at peace by this point in the game.
This second method is the most useful with Mexico during the 16th century. Make Mexico pay for its own useless forts with its gold shipments. But build only enough forts that it has an oh so slightly positive income during peace time. It'll mothball them while at peace and usually delete most of its army. During your next war, it'll eventually take a loan to enable its forts, and build a new army if threatened. Take a look from time to time and pay off a loan for a sweet liberty desire reduction.
Note that while you can use both methods on the same subject, they don't stack well, because they use different decay pools. If you use both methods, the decay will basically go twice as fast.
Also note that both of the above methods apply to any subjects, including an enormous Brandenburg March that you can get to send officers to for good measure. With Economics, you can theoretically keep the whole American continent loyal with 100% tariffs as a one province minor this way.